%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG235-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:49:53 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_1))) = mult(VAR_0,VAR_1),
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,mult(B,mult(A,B))) = mult(A,B),
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_3))) = mult(VAR_2,mult(VAR_1,mult(VAR_0,VAR_3))),
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))),
inference(clausify,[status(thm)],[c02]) ).
fof(goals,axiom,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
file('theBenchmark.p',goals) ).
cnf(c_4,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_46,plain,
mult(a,mult(b,mult(d,mult(c,mult(a,c))))) != mult(a,mult(b,mult(d,c))),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_69,plain,
mult(d,mult(b,mult(a,mult(c,mult(a,c))))) != mult(a,mult(b,mult(d,c))),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_67,plain,
mult(d,mult(b,mult(a,c))) != mult(a,mult(b,mult(d,c))),
inference(paramod,[status(thm)],[c_1,c_69]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_67,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG235-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 21:40:39 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 528404 was started by sandbox on n007,
% 0.07/0.35 % Sat Sep 26 21:40:39 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 6.
% 0.12/0.36 % Level of proof is 3.
% 0.12/0.36 % Maximum clause weight is 19.000.
% 0.12/0.36 % Given clauses 6.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------